{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Bayesian data analysis\n",
    "##  Chapter 9, demo 1\n",
    "\n",
    "Prof Gelman has a jar of coins. He promises that if the students\n",
    "guess how many coins there are, they will get all the coins in\n",
    "the jar. Students discuss and guess different values. Based on these\n",
    "they eventually present their uncertainty about the number of coins as\n",
    "a normal distribution N(160,40). What value they should guess?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "from scipy import stats\n",
    "\n",
    "%matplotlib inline\n",
    "import matplotlib as mpl\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "import os, sys\n",
    "# add utilities directory to path\n",
    "util_path = os.path.abspath(os.path.join(os.path.pardir, 'utilities_and_data'))\n",
    "if util_path not in sys.path and os.path.exists(util_path):\n",
    "    sys.path.insert(0, util_path)\n",
    "\n",
    "# import from utilities\n",
    "import plot_tools"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# edit default plot settings\n",
    "plt.rc('font', size=12)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {
    "collapsed": false
   },
   "outputs": [],
   "source": [
    "# distribution\n",
    "m = 160     # mean\n",
    "s = 40      # std\n",
    "\n",
    "x = np.arange(m-3*s, m+3*s+1)\n",
    "px = stats.norm.pdf(x, loc=m, scale=s)\n",
    "xpx = x * px"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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XfRwipM+OZkJsRpM+GJs7+7q3TRpxT4w3nTJqZLrbnTK2JwvhnB/UThwilJKa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\nKnFCCDFgVOKEEGLA/h8s0vyFFezCiAAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b7ff0db00>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(x, px)\n",
    "plot_tools.modify_axes.only_x(plt.gca())\n",
    "plt.xlim([x[0], x[-1]])\n",
    "plt.ylabel('probability')\n",
    "plt.xlabel('number of coins')\n",
    "\n",
    "# If students just want to guess right, and they do not care how much money\n",
    "# they'll get they should guess the most probable value.\n",
    "h2, = plt.plot([m, m], [0, stats.norm.pdf(m, loc=m, scale=s)])\n",
    "plt.legend(\n",
    "    (h2,),\n",
    "    ('most probable value = {}'.format(m),),\n",
    "    loc='lower center',\n",
    "    bbox_to_anchor=(0.5, 1.02)\n",
    ");"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {
    "collapsed": true
   },
   "outputs": [],
   "source": [
    "# apply gray background style\n",
    "plt.style.use(plot_tools.custom_styles['gray_background'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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UAJeHFpcB/Zps2g/YEVrXOF/VZF2LKioqIg3rK5KTkykvL9+tfTsztcvXqU0gd2sF6RlZ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\nTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b7dedda20>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# Alternatively students might want to maximize the exepected utility of the\n",
    "# number coins. Assume that utility of the money is linear.\n",
    "# Plot the utility\n",
    "plt.plot(x, x)\n",
    "plt.ylabel('utility if guess is correct')\n",
    "plt.xlabel('guess')\n",
    "plt.xlim([x[0], x[-1]])\n",
    "plt.ylim([x[0], x[-1]]);"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "collapsed": false
   },
   "outputs": [
    {
     "data": {
      "image/png": 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MbUJCQkpzcnIUmZmZNV5Xbwo7d+7ULV261Ou77767fO3atRN5eXkndDpdWeWm+Pz5833b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\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0x7f7b7ff2cf28>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "# If students guess value a, given their estimate of the uncertainity,\n",
    "# probability that they get a coins is p(a), and expected utility is a*p(a).\n",
    "# Plot the expected utility \n",
    "plt.plot(x, xpx)\n",
    "plt.ylabel('expected utility')\n",
    "plt.xlabel('guess')\n",
    "plt.ylim([0, plt.ylim()[1]])\n",
    "plt.xlim([x[0], x[-1]])\n",
    "\n",
    "# Compute the maximum of the expected utility\n",
    "mi = np.argmax(xpx)\n",
    "meu = xpx[mi]\n",
    "meux = x[mi]\n",
    "h3, = plt.plot([meux, meux], [0, meu])\n",
    "plt.legend(\n",
    "    (h3,),\n",
    "    ('guess which maximises the expected utility = {}'.format(meux),),\n",
    "    loc='lower center',\n",
    "    bbox_to_anchor=(0.5, 1.02)\n",
    ");"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.5.2"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 0
}
